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Ranjan S. Mehta, Anquan Wang∗,Michael F. Modest∗∗and Daniel C. Haworth .... The surface-HACA mechanism is consistent with the ndings of Harris and ...
MODELING OF A TURBULENT ETHYLENE/AIR JET FLAME USING HYBRID FINITE VOLUME/MONTE CARLO METHODS



Ranjan S. Mehta, Anquan Wang ,Michael F. Modest

∗∗ and Daniel C. Haworth

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

∗GE Global Research Center, One Research Circle, Niskayuna, NY 12309, USA.

∗∗ Correspondence Author, Email:[email protected]

ABSTRACT

Detailed modeling of an experimental ethylene/air jet ame is undertaken using the

composition PDF method for gas-phase kinetics coupled with detailed models for soot formation and radiation from the ames. The gas-phase kinetics is modeled using a reduced mechanism for ethylene consisting of 33 species and 205 elementary reactions. The soot formation is modeled using the method of moments with a simplied nucleation mechanism and modied surface-HACA mechanism for surface growth and oxidation. The soot formation is coupled directly with a transported PDF approach to account for turbulence–chemistry interactions in gas-phase chemistry and the highly nonlinear soot formation processes. Radiation from soot and combustion gases is accounted for by using a photon Monte Carlo method coupled with nongray properties for soot and gases. Soot particles are assumed to be small, and scattering effects are neglected. Turbulence–radiation interactions are captured accurately. Simulation results are compared with experimental data, and also with less CPU-intensive radiation calculations using the optically thin approximation.

INTRODUCTION Radiation is a dominant mode of heat transfer in many combustion systems. In numerical simulations, accurate treatment of radiative heat transfer is essential to predict ame structure correctly, which includes temperature, species and particulate matter (soot) distributions inside the ames. Most combustion devices operate in turbulent ow conditions, where turbulence–chemistry interactions (TCI) arise due to highly nonlinear coupling between temperature, species mass fractions and reaction kinetics. Much effort has been dedicated to accurately predict TCI, which remains the main goal of turbulent combustion modeling [Veynante & Vervisch 2002]. Turbulence–radiation interactions (TRI) arise from the highly nonlinear coupling between temperature and composition uctuations, which cause uctuations in radiative intensity. The effects of TRI can be comparable to those of TCI in both luminous and nonluminous ames [Cox 1977, Song & Viskanta 1987, Faeth, Gore, Chuech & Jeng 1989]. TRI has started to receive attention in recent years [Song & Viskanta 1987, Li & Modest 2002, Coelho 2007]. It has been shown that accounting for TRI can increase radiative losses from a ame by more than a factor of two [Faeth et al. 1989, Li & Modest 2002] even in nonluminous ames. Advances have been made in accurately capturing TRI in reacting ows using transported PDF methods [Mazumder & Modest 1999, Li & Modest 2002, Tessé, Dupoirieux & Taine 2004, Wang & Modest 2007b]. Recently Wang and Modest [2007b] developed an advanced Photon Monte Carlo method for spectral radiative calculations, applied to reacting and nonreacting ows. The method uses accurate line-byline absorption coefcients for combustion gases like CO2 and H2 O and has been extended to include

nongray radiation due to soot. This method allows capture of TRI arising from correlations between absorption coefcient and local Planck function (emission TRI) and also between absorption coefcient and incident radiation (absorption TRI).

PHYSICAL AND NUMERICAL MODELS

Gas-phase Kinetics

A systematically reduced 33 species ethylene mechanism containing 205 ele-

mentary reactions is used to model gas-phase kinetics [Law 2005]. The molecular transport properties and thermochemistry have been implemented using TRANSPORT [Kee, Dixon-Lewis, Warnatz, Coltrin & Miller 1986] and CHEMKIN-II [Kee, Rupley & Miller 1989], respectively, and interfaced seamlessly with the underlying CFD code [Zhang & Haworth 2004].

Soot Model

Soot emission can dominate gas radiation by more than a factor of ten when soot is

present at ppm levels [Modest 2003]. It has been shown that, in the presence of soot, peak temperatures can drop by more than 300K due to soot radiation [Bandaru 2000]. Thus accurate prediction of soot levels is essential when modeling sooting ames. In addition, the temperature eld affects kinetic rates of most gas-phase reactions and soot-subprocesses, thereby changing the ame structure signicantly. Detailed and semi-detailed soot models generally have two parts: i) soot kinetics (interaction between soot particles and the surrounding gas-phase species) that includes nucleation, surface growth and oxidation models; and ii) soot-particle dynamics (interaction between the soot particles) that includes coagulation and aggregation. The soot particle dynamics can be treated in different ways. These include the method of moments where one solves for the moments of the particle-size distribution function (PSDF) [Frenklach 2002], or sectional methods [McEnally, Schaffer, Long, Pfefferle, Smooke, Colket & Hall 1998] where the PSDF is divided into discrete sections by average particle size. Here a method of moments with interpolative closure has been used. Three to six moments have been found to be sufcient in previous modeling studies of laminar premixed ames [Frenklach & Wang 1994, Appel, Bockhorn & Frenklach 2000] and opposed-ow diffusion ames [Wang, Du, Sung & Law 1996]. The method of moments can be extended to aggregation of soot particles into mass fractals [Kazakov & Frenklach 1998]. Since the current study is limited to atmospheric-pressure ames, it is expected that soot particles will remain primarily spheroidal; hence aggregation is not considered.

Soot kinetics.

Soot formation is a complex process and can be divided into several subprocesses: i)

nucleation of soot particles, when they acquire characteristics different from the gas-phase; ii) surface growth/oxidation of soot particles due to reactions with the gas-phase and iii) particle coagulation/aggregation due to collisions with each other. All these processes occur simultaneously and need to be modeled accurately [Bockhorn 1994]. Much research has been done in past decades on the nature of soot nucleation, and many models have been put forth [Kennedy 1997]. It is generally accepted that soot particles are nucleated after formation of large polycyclic aromatic hydrocarbon (PAH) molecules. However, nucleation models based on large molecules require these to be included in the gas-phase thermochemistry [Frenklach & Wang 1994], resulting in large gas-phase mechanisms containing hundreds of species [Appel et al. 2000].

These large mechanisms are computationally

prohibitive for simulating turbulent ames and alternative models are of interest. In the case of nonpremixed ames burning in atmospheric conditions, it has been observed that most contributions to

soot mass are due to surface reactions and are relatively insensitive to nucleation models [Leung, Lindstedt & Jones 1991, Mehta, Haworth & Modest 2008]. Here a simplied nucleation mechanism based on local acetylene (C2 H2 ) concentration proposed by Leung, Lindstedt and Jones [1991] has been used; this has been shown to work well in turbulent ames as well [Lindstedt & Louloudi 2005, Mehta, Haworth & Modest 2007]. Soot surface growth models have been an active area of research for several decades [Kennedy 1997]. Frenklach and Wang [1991, 1994] proposed chemical similarity, which postulates that chemical reactions taking place on the soot particle surface are analogous to those for large PAH molecules [Frenklach & Wang 1991]. The surface-HACA mechanism is consistent with the ndings of Harris and Weiner [1985], who determined that acetylene dominates surface growth in their ames.

Soot surface oxidation

is due to attack by OH radicals and oxygen [Neoh, Howard & Sarom 1981].

Here the surface-

HACA mechanism has been used [Frenklach & Wang 1994]. The key reactions involved in surface growth/oxidation of soot particles are listed in Table 1.

Surface Growth Mechanism

Table 1. No.

Here



Reaction

1

Cs + H

2

Cs + OH

References

¿ Cs∗ + H2

[Frenklach & Wang 1994, Appel et al. 2000]

¿ Cs∗ + H2 O

[Frenklach & Wang 1994, Appel et al. 2000]

∗ +H →C

3

Cs

4A

Cs + C2 H2

→ Cs + H

[Frenklach & Wang 1994]

4B

Cs + C2 H2

→ Cs∗ + H

[Wang et al. 1996]

∗ +O

[Frenklach & Wang 1994]

s

→ 2CO + products

5

Cs

6

Cs + OH

2

→ CO + products

[Frenklach & Wang 1994] [Neoh et al. 1981, Frenklach & Wang 1994]

indicates an irreversible reaction and

¿

denotes a reversible reaction, Cs denotes a soot

∗ particle and Cs is a soot radical. The kinetic rate coefcients for each of the reactions and other details can be found in the references listed in the table.

Soot particle dynamics.

The time evolution of a particle ensemble is described by population balance

equations known as the “Smoluchowski master equations” [Fuchs 1989, Seinfeld & Pandis 1998]. These can be written as,

dN1 dt

dNi dt

=

1 2



= − ∑ β1, j N1 N j

(1a)

j =1

i−1



j =1

j =1

∑ β j,i− j N j Ni− j − ∑ βi, j NiN j

i

= 2 . . . ∞.

(1b)

Here Ni denotes the number of particles of size i per unit volume: i.e., size i particle number density.

βi, j is the collision coefcient between particles = βi, j (Ni , N j , mi , m j ) where mi is the mass of particle of size i.

N1 is the number density of the smallest particles and of size i and j. In general, then,

βi, j

The concentration moment of the particle number density function Ni is



Mr

= ∑ mri Ni .

(2)

i=1

= 0,

= ∑∞ Ni i=1

is the total particle number density. For r = 1, M1 = m N is the total mass of particles per unit volume, so that the volume fraction is given by f v = ∑∞ i i i=1 M1 /ρs , where ρs is the density of soot particles. Higher order moments may lack a simple physical

It can be seen that if r

then M0

interpretation but are needed for accuracy. (r

It can be seen that knowledge of all integer moments

= 0, . . . , ∞) is equivalent to knowledge of the size distribution function itself.

However, most of the

principal properties for the particle ensemble can be deduced from the rst few moments. Nucleation, surface growth and particle coagulation equations are then cast in those for the moments of the PSDF in the following form.

dMr dt

= Rr + Gr + Wr

r

= 0, 1, . . . Mmax .

(3)

where Rr is source due to nucleation, Gr due to coagulation, Wr due to surface reactions and Mmax is the number of moments retained in the formulation. Unclosed terms appearing in these equations are closed using an interpolative closure whose details can be found in Frenklach [2002]. Here Mmax

=5

is used and is expected to sufce. At higher pressures, soot coagulation results in formation of mass fractals that have geometries far from spheroidal [Kazakov & Frenklach 1998]. However, since the current study is limited to atmospheric-pressure ames, it is expected that soot particles will stay mainly small and spheroidal. This assumption was found to be sufcient in turbulent ames simulated by Lindstedt and Louloudi [2005]. Soot coagulation is considered in free-molecular, continuum and transition regimes. The surface reaction rate due to gaseous species (growth or oxidation) for a soot moment r can be written as, r −1

surf Wr

= ksgCg αχs M0 ∑

k =0

µ ¶ r

k

∆mr−k µr+2/3

(4)

where ksg is the kinetic rate coefcient for reaction with gas g, Cg is the molar concentration of the gas species,

α

is a steric factor,

χs

is the nominal number density of surface radical sites,

∆m

is the

change in soot mass due to the reaction [Frenklach & Wang 1994] and µ p is the reduced soot moment. The factor

α is the fraction of the surface sites available for chemical reactions; it was introduced by

Frenklach and Wang [1991] to account for differences in soot surface growth rates with temperature as a result of structural changes. The functional form for

α has evolved from constant values [Frenklach

& Wang 1994, Colket & Hall 1994] to a temperature-dependent expression used by Appel, Bockhorn and Frenklach [2000]. Here

α = αABF00 , corresponding to the functional form introduced by Appel,

Bockhorn and Frenklach [Appel et al. 2000] has been used. The authors are not aware of previous application of

αABF00 to turbulent diffusion ames.

Radiation Models

In low-Mach-number ows, radiation does not alter conservation of mass, mo-

mentum and species conservation. However, the energy (absolute enthalpy) equation is modied by the presence of a radiative source term:

∂u j ∂J h D p ∂ρh ∂ρhui + =− i + + τi j + Sradiation ∂t ∂xi ∂xi Dt ∂xi

(5)

h

where h is the absolute enthalpy, Ji denotes the molecular transport of enthalpy and Sradiation is the radiative source term interpreted as the local net volumetric gain of thermal energy due to both emission and absorption, and can be expressed as [Modest 2003]

Sradiation

where q

R

is the radiative ux,

R

= −∇ · q =

Z ∞

µZ κη

0





Iη d Ω − 4πIbη



(6)

κη = κη (Y , T , p), is the spectral absorption coefcient of the radiating

medium (mixture), which may be a function of temperature T and species concentrations (expressed as mass fractions) of the radiating medium Y . Iη is the spectral radiative intensity, and Ibη is the Planck function or spectral blackbody intensity. The subscript

η

denotes spectral dependence and



is the

solid angle. Radiation heat transfer plays a dominant role in most industrial ames, and is governed by a complex integrodifferential equation in ve dimensions [Modest 2003]. In addition, the spectral behavior of the absorption coefcient of the medium depends on its composition and local concentrations of selectively-absorbing/emitting combustion gases like water vapor, carbon dioxide and particulate matter like soot. The simplest approximation for the radiative source term is the so-called optically thin assumption, in which local re-absorption of radiation is neglected, and spectrally integrated absorption coefcients can be used for gases and soot, resulting in a simplied expression for the radiative source term given by

Ã

!

i=Ngas

Sradiation

=



k p,i Pi + k p,soot

¡

4σSB T

i=1

4

4 − Tsurr

¢

(7)

where k p,i is the Planck-mean absorption coefcient of radiating gases such as H2 O and CO2 , in m

−1 bar −1 , P is the partial pressure of species i in bar, and k i p,soot is the Planck-mean absorption

coefcient of soot. Here we use Planck-mean, (k p,soot ), and

κsoot ,η

spectral values based on Rayleigh

theory [Modest 2003], assuming small particles, and a complex index of refraction based on Chang and Charalampopulous [1990]. Tsurr

= 300K is used in the modeling.

For a more accurate evaluation of the radiative source term it is necessary to solve the nongray RTE, which has been done with various methods, including: i) the spherical harmonics method or a variation of it [Mazumder & Modest 1999, Li & Modest 2002]; ii) the discrete ordinates method (nite volume method) [Coelho, Teerling & Roekaerts 2003] and iii) variants based on the Photon Monte Carlo (PMC) method [Tessé et al. 2004, Snegirev 2004, Wang & Modest 2007a]. One powerful feature of the PMC method is that it can handle problems of high complexity with relative ease. For a variety of combustion applications, where joint probability-density-function (PDF) methods [Pope 1985] are used, the medium is represented by notional particles evolving with time and traditional Monte Carlo ray-tracing schemes developed for continuous media are no longer useful for such stochastic media.

Recently, Wang and Modest [2006] developed several emission and absorption

schemes for media represented by discrete particles. The method was extended to achieve line-byline accuracy in radiative property calculations with little increase in computational cost [Wang & Modest 2007b].

The PMC simulates the process of emitting radiation by releasing representative

photon bundles (rays) in random directions, which are traced until they are absorbed (completely) at certain points in the medium or escape from the domain. An energy-partitioning scheme is utilized which reduces statistical error, compared to standard Monte Carlo [Modest 2003]. In media represented by discrete particles, the ray energy is distributed over all the particles that the ray interacts with, if the energy-partitioning method is employed [Wang & Modest 2006].

Turbulent Closure

Transported PDF methods have been developed over the past few decades for re-

acting as well as nonreacting turbulent ows through the work of several researchers (see Pope [1985] and references therein). Composition PDF methods are a class of transported PDF methods, where physical scalars including temperature (or absolute enthalpy) and species concentrations are treated as random variables. The joint PDF of these is then a function of spatial location x and time t , whose transport equation can be derived [Pope 1985] and takes the form,

∂F ∂ ∂ hD 00 E i ∂ ∂ ui F ]+ [Sα,reac (ψ)F ] = − + [e ui |ψ F + ∂t ∂xi ∂ψα ∂xi ∂ψα

·¿

À ¸ ∂Jiα ∂ |ψ F − [Sα,rad (ψ)F ] ρ ∂xi ∂ψα 1

(8) In Eq. (8), summation is implied over repeated indices i and

α

within the terms with i and

resenting physical and composition space, respectively. The notation

hA|Bi

α

rep-

denotes the conditional

probability of event A given that B occurs. The rst two terms in Eq. (8) are transport of the mass density function

F

transported with the Favre-averaged mean ow. The third term is ux in compo-

sition space due to sources that depend only on local composition (e.g., chemical reaction rates and radiative emission). This equation also shows that, no matter how nonlinear these sources are, they can be represented exactly. Terms on the right-hand side must be modeled. The rst two terms represent transport in physical space due to turbulent diffusion and transport in composition space due to molecular-level mixing. Turbulent diffusion is commonly modeled based on the gradient-diffusion hypothesis as,

D

00

ui |ψ

The turbulent diffusivity

Γt

E F

' Γt

∂F ∂xi

(9)

is estimated by an ad-hoc relationship that is derived from dimensional

analysis and other considerations [Pope 1985], so that

Γt = Cµ hρi σφ k2 /ε = µT σφ

(10)

σφ are, respectively, the modeled turbulent diffusivity (e.g., obtained from the standard two-equation k-ε model) and a turbulent Schmidt or Prandtl number. where, µT and

Various mixing models have been used to model the second term on the right-hand side of Eq. (8). In the current work, the Euclidean Minimum Spanning Tree (EMST) model by Subramaniam and Pope [1998] is used, which has been shown to perform better than other popular models in nonpremixed combustion.

In principle, the PDF transport Eq. (8) can be solved by traditional nite-

volume and nite-element methods.

This approach was used by Janicka et al. [Janicka, Kolbe &

Kollmann 1978] for a jet diffusion ame. In general, however, the PDF is a function of a large number of independent variables, which makes it prohibitively expensive to use standard nite volume methods (FVM) and nite element methods (FEM). Monte Carlo approaches to the solution of the PDF equation have therefore been developed ( [Pope 1985]). The basic idea is to represent the PDF by a sufciently large number of notional uid particles. The mean quantities at any point in the domain are then calculated as an ensemble average over the particles in a sufciently small neighborhood. In principle, the particle tracking method is grid-free; however, in general, a grid is required to extract the statistics of the scalars at discrete locations. The algorithm presented here was developed by Pope and coworkers [Pope 1985, Muradoglu, Jenny, Pope & Caughey 1999, Jenny, Pope, Muradoglu & Caughey 2001] and by Subramaniam and Haworth

[2000]. An algorithm developed by Zhang

and Haworth [2004] to ensure consistency between the values obtained by a FV solution and Monte

Carlo solution is also implemented. All use a coupled ow solver to provide information about the velocity eld. The numerical methods have been analyzed for different types of errors by Pope and coworkers( [Xu & Pope 1999, Muradoglu, Pope & Caughey 2001]). The third term on the right-hand side of Eq.(8) is due to radiative transfer (i.e., the difference between energy gain due absorption of incident radiation and energy loss due to local emission):

Srad

where

=

Z ∞ 0

Z

κη (Gη − Ib,η )d η,



=



Iη d Ω,

(11)

κη is the local spectral absorption coefcient, Ibη is the local (spectral) blackbody intensity, and κη and Ibη are functions of

Gη is the incident radiative intensity integrated over all directions. Both

local composition variables only and, therefore, local emission can be evaluated exactly using composition PDF methods. In contrast, Gη depends on properties at every (other) point in the domain and one-point PDFs are not sufcient to close the absorption term in turbulent ows. The PDF transport equation (8) is usually solved using particle Monte Carlo methods, in which the PDF is discretized into a sufciently large number of “notional” (stochastic) particles, which are traced through the entire domain. Each particle represents a ow realization, so that the instantaneous particle eld can be regarded as a snapshot of real ow [Wang & Modest 2007a]. Therefore, a PMC method can be

­

®

employed to evaluate both the local emission ( 4πκη Ib,η ) and the absorption of incident radiation (

­

κη Gη

®

) exactly without any futher modeling assumptions. Emission is fundamentally closed us-

ing the one-point PDF and does not require modeling. Therefore it is evaluated correctly even when considering optically thin radiation. The PMC model allows accurate determination of both emission and absorption TRI within statistical limits and does not need any other modeling assumptions (like negligible absorption TRI etc.). Here the composition PDF method has been extended to include soot scalars (moments) as part of composition space, so that exact turbulent closure is obtained also for the highly nonlinear soot subprocesses. The required mean velocity elds in Eq. (8) are obtained using standard a k-ε model.

FLAME CONFIGURATION A turbulent jet ame studied experimentally by Coppalle and Joyeux [1994] with a jet Reynolds number of 11, 800 has been simulated. This ame has been studied numerically by Lindstedt and Louloudi [2005] using optically thin radiation. The effect of re-absorption on temperature predictions and soot yield was left as an open question. In addition, their solution method for scalar transport was a parabolic time-marching scheme, which is not generally extendable to complex congurations. Empirical models were used for all the soot subprocesses including surface growth and oxidation. Here an elliptic solution method is employed for scalar transport (including soot moments), which can be easily applied to complex congurations. A weak co-ow is used instead of simulating a jet ame into quiescent air, and a small false pilot is employed to stabilize the ame. The jet diameter is dj

= 4mm with fuel velocity of 29.5m/s.

A three-dimensional wedge-like grid system is employed to

simulate the axisymmetric ame by applying periodic boundary conditions on the sides as shown in



Fig. 1, with a wedge angle of 10 ; the dimensions in x- and z- directions are 30d j and 250d j , respectively. The grid is ne near the fuel jet to accurately resolve large local gradients in the mixing region and coarser in the coow air region to save computational time. With composition PDF methods it is found that around 30 particles per cell on average are sufcient to resolve the turbulent uctuations in the ame. For radiation, following [Wang & Modest 2007a] the rays are traced as cones with 1

◦ opening angles

and 200, 000 rays are traced per time step. Since the ames are statistically stationary, time-averaged radiative source terms evaluated for each cell are fed back to the FV code. In traditional FV methods, the residual error diminishes to zero with sufcient number of iterations, and can be used to monitor

X

X

Y

Figure 1.

Z

Y

Z

Grid used in simulation

1800 80 1600

60 1400

Average T Average T fluctuations

40

20

1200

1000 5000

10000

15000

Average emission weighted temperature (K)

Average fluctuations in temperature T’’V (K)

100

20000

Time step

Figure 2.

Progress of convergence criteria for PDF/Monte Carlo simulation

convergence. However, the residual error in hybrid FV/Monte Carlo method cannot show the same behavior due to presence of statistical noise. Hence a different metric is generally used to monitor convergence; following the approach of Wang and Modest [2007a], emission-weighted average tem-

D

perature (Te ) and volume-averaged root-mean-square (rms) uctuations ( T

00

convergence, i.e.,

R Te

= RV V

D

5

k p T dV k p T 4 dV

and

T

00

= v

1 V

∑ c

Vc

ρc

v

)are used to monitor

#1/2

"

E

E

∑m

p

(Tp − Tc )2

Vc ,

(12)

p∈c

where the outer sum denotes summation over cells, and the inner sum is over particles inside a cell.

Z

Z

a)

b) 250

250 Y

Y

T

Fv

200

100

50

X/dj

150

100

50

0

Figure 3.

20

0 100 50

0

Y

0

1.3E-06 1.2E-06 1.1E-06 1E-06 9E-07 8E-07 7E-07 6E-07 5E-07 4E-07 3E-07 2E-07 1E-07

0

R/dj

R/d20 j

5 00 100

Y

X/dj

150

200

1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400

Mean temperature and soot volume fraction contours

2000

Temperature (K)

1500

1000

T (no soot radiation) T (optically thin) T (with re-absorption) Exp. (Coppalle and Joyeux)

500

0

0.2

0.4

0.6

0.8

1

Distance from jet (m) Figure 4.

Measured and computed centerline mean temperature proles using optically thin radiation

and PMC method

RESULTS AND DISCUSSION The simulations are run in a transient fashion until the convergence criteria are no longer changing with time, using a timestep of

∆t = 50 µs.

Convergence results are shown in Fig. 2 using the PMC as

RTE solver, but are similar when using the optically thin approximation. Figure 3 shows the converged steady-state contours of the mean temperature and soot volume fraction using the PMC. The contours show reasonable distribution of soot commensurate with the ame structure. The computed centerline mean temperature proles obtained without soot radiation, and with soot radiation using either the optically thin approximation or the PMC are shown in Fig. 4. It can be seen that soot radiation has a large effect on the temperatures and, consequently, on the entire ame structure. The peak centerline mean temperature drops by more than 300K from 1920K to 1600K in the case of optically thin radiation. Thus, optically thin radiation under-predicts peak temperature compared to the experimentally measured value of 1665K. Optically thin radiation results also underpredict temperatures in most of the downstream region. This fact has important implications on soot formation and oxidation rates, thereby changing the soot proles. Using the PMC, (thus accounting for

2E-06 Fv (optically thin) Fv (with re-absorption) Exp. (Coppalle and Joyeux)

Soot volume fraction

1.5E-06

1E-06

5E-07

00

0.2

0.4

0.6

0.8

1

Distance from jet (m)

Figure 5.

Measured and computed centerline mean soot volume fraction proles using optically thin

radiation and PMC method

re-absorption) results in a peak temperature of 1678K, which is closer to the experimentally reported peak axial value. Therefore, accounting for re-absorption is necessary when modeling sooting ames of this size. An important observation is that the change in temperature elds affects the soot levels, which in turn affects the amount of heat radiated from the ame. The global (volume-integrated) emission, absorption, total heat loss and the radiant fraction (compared to chemical heat release) are listed in Table. 2. It can be seen that using the optically thin assumption, results in a higher radiant fraction and relatively low temperatures. With re-absorption, the emission is higher due to higher temperatures, but almost 15% of the emitted energy is re-absorbed in the domain. The radiant fraction is high compared to typical values found in nonsooting ames.

Table 2. Description

Global emission, absorption and radiant fraction Total

Total Ab-

Radiative

Radiant

Emission

sorption

Loss (W)

Fraction (%)

(W)

(W)

Optically Thin

6070

–

6070

28.9

PMC (with re-

6588

964

5624

26.7

absorption)

The predicted centerline mean soot levels are compared with experiment in Fig. 5. It can be seen that the change in ame structure also affects the soot predictions. The peak axial soot volume fraction is slightly lower than experiments when using both optically thin and PMC models. However, considering the ppm levels of soot, the agreement is very encouraging. Re-absorption results in higher temperatures, which increase both surface growth and oxidation rates, and local conditions dictate the net effect on the soot growth rates. In the current ame accounting for re-absorption results in a higher soot formation rate, giving better agreement with experiments. Radial soot volume fractions at two different stations are shown in Fig. 6. It can be seen that predictions follow the trend of experiments. At both stations optically thin radiation model underpredicts soot to a greater extent than when accounting for re-absorption. Both models are able to capture the off-center peak location reasonably;

Soot volume fraction

Exp. (Coppalle and Joyeux) with re-absorption optically thin

6E-07

X=0.234 m 4E-07

2E-07

0

0.02

0.04

0.06

0.08

Soot volume fraction

2E-06 8E-07

Experiment with re-absorption optically thin

1.5E-06

X=0.347 m

1E-06

5E-07

0

0

0.02

Distance from axis (m)

Figure 6.

0.04

0.06

0.08

Distance from axis (m)

Measured and computed radial soot volume fraction proles at two axial stations

agreement is better at downstream location compared to upstream.

CONCLUSION A composition PDF method coupled with a detailed soot model was used to simulate a turbulent ethylene/air jet ame. Detailed radiation calculations were undertaken, using both optically thin radiation (neglecting re-absorption) and with spectral (nongray) photon Monte Carlo method. The effects of using different radiation models were studied based on predicted temperature and soot volume fraction proles. It was found that accounting for re-absorption is very important in case of sooting ames. Using a composition PDF method to account for TCI accurately along with the PMC method for capturing TRI provides a powerful approach to model turbulent reacting ows, in general. The method can be extended to complex congurations and even industrial- scale problems. Soot predictions are dependent on temperatures and vice-versa and therefore, the exact effects of TRI and TCI on the ame structure cannot be separated. Separation of the relative importance of emission TRI and absorption TRI in sooting ames has also not been undertaken. These are topics of ongoing research.

ACKNOWLEDGMENT This work was supported by NASA under grant number NNX07AB40A.

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